% $OpenXM: OpenXM/src/R/r-packages/hgm/man/hgm.cwishart.Rd,v 1.3 2013/03/08 07:32:28 takayama Exp $ \name{hgm.cwishart} \alias{hgm.cwishart} %- Also NEED an '\alias' for EACH other topic documented here. \title{ The function hgm.cwishart evaluates the cumulative distribution function of random wishart matrix. } \description{ The function hgm.cwishart evaluates the cumulative distribution function of random wishart matrix of size m times m. } \usage{ hgm.cwishart(m,n,beta,x0,approxdeg,h,dp,x,mode,method,err) } %- maybe also 'usage' for other objects documented here. \arguments{ \item{m}{The dimension of the Wishart matrix.} \item{n}{The degree of freedome (a parameter of the Wishart distribution)} \item{beta}{The eigenvalues of the inverse of the covariant matrix /2 (a parameter of the Wishart distribution). The beta is equal to inverse(sigma)/2. } \item{x0}{The point to evaluate the matrix hypergeometric series. x0>0} \item{approxdeg}{ Zonal polynomials upto the approxdeg are calculated to evaluate values near the origin. A zonal polynomial is determined by a given partition (k1,...,km). We call the sum k1+...+km the degree. } \item{h}{ A (small) step size for the Runge-Kutta method. h>0. } \item{dp}{ Sampling interval of solutions by the Runge-Kutta method. } \item{x}{ The second value y[0] of this function is the Prob(L1 < x) where L1 is the first eigenvalue of the Wishart matrix. } \item{mode}{ When mode=c(1,0,0), it returns the evaluation of the matrix hypergeometric series and its derivatives at x0. When mode=c(1,1,(m^2+1)*p), intermediate values of P(L1 < x) with respect to p-steps of x are also returned. Sampling interval is controled by dp. } \item{method}{ rk4 is the default value. When method="a-rk4", the adaptive Runge-Kutta method is used. Steps are automatically adjusted by err. } \item{err}{ When err=c(e1,e2), e1 is the absolute error and e2 is the relative error. As long as NaN is not returned, it is recommended to set to err=c(0.0, 1e-10), because initial values are usually very small. } } \details{ It is evaluated by the Koev-Edelman algorithm when x is near the origin and by the HGM when x is far from the origin. We can obtain more accurate result when the variables h is smaller, x0 is relevant value (not very big, not very small), and the approxdeg is more larger. A heuristic method to set parameters x0, h, approxdeg properly is to make x larger and to check if the y[0] approaches to 1. % \code{\link[RCurl]{postForm}}. } \value{ The output is x, y[0], ..., y[2^m] in the default mode, y[0] is the value of the cumulative distribution function P(L1 < x) at x. y[1],...,y[2^m] are some derivatives. See the reference below. } \references{ H.Hashiguchi, Y.Numata, N.Takayama, A.Takemura, Holonomic gradient method for the distribution function of the largest root of a Wishart matrix \url{http://arxiv.org/abs/1201.0472}, } \author{ Nobuki Takayama } \note{ %% ~~further notes~~ } %% ~Make other sections like Warning with \section{Warning }{....} ~ \seealso{ %%\code{\link{oxm.matrix_r2tfb}} } \examples{ ## ===================================================== ## Example 1. ## ===================================================== hgm.cwishart(m=3,n=5,beta=c(1,2,3),x=10) ## ===================================================== ## Example 2. ## ===================================================== b<-hgm.cwishart(m=4,n=10,beta=c(1,2,3,4),x0=1,x=10,approxdeg=20,mode=c(1,1,(16+1)*100)); c<-matrix(b,ncol=16+1,byrow=1); #plot(c) } % Add one or more standard keywords, see file 'KEYWORDS' in the % R documentation directory. \keyword{ Cumulative distribution function of random wishart matrix } \keyword{ Holonomic gradient method } \keyword{ HGM }